Problem: Solve for $x$ and $y$ using elimination. ${-3x-2y = -20}$ ${5x+2y = 32}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $-2y$ and $2y$ cancel out. $2x = 12$ $\dfrac{2x}{{2}} = \dfrac{12}{{2}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {-3x-2y = -20}\thinspace$ to find $y$ ${-3}{(6)}{ - 2y = -20}$ $-18-2y = -20$ $-18{+18} - 2y = -20{+18}$ $-2y = -2$ $\dfrac{-2y}{{-2}} = \dfrac{-2}{{-2}}$ ${y = 1}$ You can also plug ${x = 6}$ into $\thinspace {5x+2y = 32}\thinspace$ and get the same answer for $y$ : ${5}{(6)}{ + 2y = 32}$ ${y = 1}$